Memeorandum

February 06, 2005

Let's Help Paul Krugman With An Economic Forecast

Paul Krugman misinterpreted some economic forecasts, and consequently falsely besmirched the reputations of the advocates of Social Security privatization (Is it an odd-numbered day? I am one!). On behalf of both Truth and the Besmirched, I stand ready to provide a bit of assistance with some economic modeling.

Let me inflict some of those numbers on you. Sorry, but this is important.

Schemes
for Social Security privatization, like the one described in the 2004
Economic Report of the President, invariably assume that investing in
stocks will yield a high annual rate of return, 6.5 or 7 percent after
inflation, for at least the next 75 years. Without that assumption,
these schemes can't deliver on their promises. Yet a rate of return
that high is mathematically impossible unless the economy grows much
faster than anyone is now expecting.

...Which brings us to the privatizers' Catch-22.

They can rescue
their happy vision for stock returns by claiming that the Social
Security actuaries are vastly underestimating future economic growth.
But in that case, we don't need to worry about Social Security's
future: if the economy grows fast enough to generate a rate of return
that makes privatization work, it will also yield a bonanza of payroll
tax revenue that will keep the current system sound for generations to
come.

Alternatively, privatizers can unhappily admit that future
stock returns will be much lower than they have been claiming. But
without those high returns, the arithmetic of their schemes collapses.

Is that clear - according to Prof. Krugman, we need high growth to get a high return on capital, and good stock market performance.

This notion certainly has strong intuitive appeal. Most folks who think about the stock market have learned that low growth is bad for profits and sales, and high growth is good; extending that intuition over the next 75 years seems to produce the obvious result described by Prof. Krugman.

However, intuition is not analysis. What went wrong here? For most people, "low growth" mentally translates into "growth below expectations"; high growth becomes "growth above expectations". But there is no reason that a stable, no-growth economy can not have a stable, positive, attractive rate of return, as we illustrate at painful length here. Folks who like to think in terms of financial instruments will remember that a Treasury bond provides no growth at all, but a very stable return.

So what happened with the forecasts used by the Social Security trustees? Well, folks who reflect upon economic forecasts will agree that the return on capital projected by an economic forecast is highly sensitive to the method used to forecast the return on capital. Hmm, does that strike you as painfully obvious? Let me elaborate.

It turns out that growth is not the issue Prof. Krugman think it is. I will grant that the low growth scenario presented by the Social Security Trustees may imply a low return on capital. However, using the modeling method assumed by Dean Baker, economic growth is not a solution.

Economic growth comes from growth in either the size of the labor force, or an increase in the productivity of each worker. Each worker requires new capital, at the same level as current workers. (Beyond that, higher productivity requires capital "deepening", which amounts to more capital per worker - this adjustment makes the Krugman error even more glaring, however).

So, we can get more growth out of economy by bringing in more workers. If, for example, the labor force grows by an additional 1% per year, GDP will also grow by an additional 1% per year. The payroll tax base will rise, and Social Security will be "saved". High growth is good!

But wait - does that new high growth forecast actually imply a higher return on capital? Not as Dean Baker modeled it; new workers require new capital, and the return on capital remained the same as in the original low-growth forecast. This, by the way, is a common-sense result - if a factory with 100 workers manning 100 drill presses sells 100 units and produces a 5% return on capital, then 200 workers manning 200 drill presses should produce 200 units for sale, but the return on capital will still be 5%. Lots of growth, but the return on capital does not change.

Maybe he did, but that does not help, as modeled by the Soc Sec trustees and interpreted by Dean Baker. Higher productivity means that there is more output per worker. However, the question instantly arises, who captures the benefit of that increased return? A very common assumption in economics is that workers capture most of that benefit - skilled workers get raises. Higher productivity results in higher growth, but the return on capital does not change; instead, real wages rise.

This outcome can "save" Social Security - the higher wages result in higher payroll tax receipts today (and higher benefits indexed to the wages down the road, but we are moving quickly over a lot of ground here. No, really, this IS quick.) However, even though Social Security is "saved", returns on capital continue to be dismal, as per the original assumptions.

In my factory example above, the 100 workers have a productivity surge and produce 105 units. In the short run, the owner may benefit by pocketing the profit on the additional 5 units. Eventually, however, competitive forces will prompt him to offer the workers raises, or see them leave. That, at least, is the gist of how it has been modeled here.

So, you may be thinking, if the high growth forecasts that "save" Social security don't also "save" the stock market by implying higher returns on capital, why did Prof. Krugman say they did, and is it hopeless for stocks?

As to how Prof. Krugman made an error he would not tolerate from one of his grad students, I have no idea. But the stock market question is easily answered - now that we know that growth, per se, is not the issue, we know where to look - if you want to forecast higher capital market returns, you need to figure out what, in the model, is guiding capital returns. Tweak that, contemplate the implications, and there you are.

Eventually, the analysis will come back to the income share earned by capital. The Social Security trustees assumed it would remain constant; Dean Baker's astute observation [Link, please!] was that, given the current earnings yield and the requirement for new capital, the assumption that the income share to capital was constant led to some fairly gloomy implications for share prices.

Problem solved - we need to raise the return on capital by projecting that capital will earn more. Can we do that in a low growth scenario? Sure.

Suppose the work force grows even more slowly than the low growth scenario because a (daft) Congress cracks down on immigration. Fewer workers, less growth, less payroll taxes, and an earlier problem date for Social Security.

Meanwhile, Benedict Arnold CEOs use the threat of outsourcing to hold down wage increases. Is that implausible? It sounds like the Kerry campaign (feel free to tell me he was implausible). And no, I don't think it would represent a long run equilibrium for the US economy. But during a transition period, the income share of capital could be modeled to rise from, e.g., 8% to 10%. Throw in some foreign profits from the newly outsourced jobs, and equity returns can look pretty good.

Let's be clear - I am identifying, not advocating. Prof. Krugman insisted, in his column, that growth and capital returns went hand in hand, and implied that privatizers were playing a bit of a shell game with the public. In fact, he was wrong, and there are plausible low-growth scenarios that hammer Social Security but are good for stocks.

I hope that sets the record straight (what are the odds?). There are still plenty of other reasons to support or oppose Social Security privatization (and Republicans are not touting the stock market anyway.

I would like to thank Dean Baker, whose underlying idea was quite insightful. He has been a good sport and provided some useful guidance in an earlier comments thread. I should also find a more useful link, but, incredibly, other duties call.

Comments

To be honest you are a bit confusing. Well, either that or I don't understand you but I'd rather go with the first explanation! :)

It seems you are saying that you can have low growth and high returns. I think the flaw in your model is that you don't take into account the need for investment to replenish capital. http://www.j-bradford-delong.net/movable_type/2005-3_archives/000290.html>Brad Delong talks about that and how Andrew Samwick's model requires businesses to spend 150% of earnings in cash flows to shareholders. That won't last long.

But even if your model worked in theory you have not explained why we should think it likely. Krugman appears to be perfectly correct when he says that there is a shell game here. The public forecasts that show SS in troublw all have low growth assumptions. The public forecasts that I have seen that lead to high stock returns are all based on high growth. That is a shell game.

You would have a point that Krugman was wrong in talking about a shell game if you could point to public forecasts by any of the leading privatization proponents (specially from the WH) that predict high stock returns yet low economic growth.

Great analysis, save a step. Assume Krugman is right: high returns equal a high rate of growth and therefore a "bonanza of payroll tax revenues". Given that Social Security payments are indexed to wage growth, those high payroll tax revenues will be correlated with much higher payouts per Social Security recipient, leaving the system, again, in a massive deficit.

Of course, Krugman knows this, but it is mucks up his argument. So, like all other inconvenient facts, into the trash it goes.

Sure, it is possible we could grow our way out of the Social Security problem, but ONLY if we adjust the rate of growth of payouts. Somehow, I think Krugman will not approve of such a change if it is suggested by a politician with an (R) after his name.

I don't think you're quite understanding what I mean by 'in trouble', GT. While under some scenarios, higher wage growth can maintain the SS system as is, that is only by decreasing the returns to the workers' on their payroll taxes.

Btw, is it not odd that Prof. DeLong's reply (odd in itself, in seemingly not realizing what 'depreciation' does to corporate profits) to Andrew Samwick's Krugman's Unhappy Returns, doesn't have comments open?

I must say that my poor eyes glazed over reading your excellent analysis of how the Krugman gets his economics worng. But that doesn't dimish the fact that you own the numbers game on Social Security reform. Over on my blog I've been covering the debate on more philosophic grounds. To me, reform is a moral battle. One that pits government control agaisnt freedom and personal responsibility. I'll be sure to keep reading your blog for the numbers analysis.

No Patrick, that is not what the SSA says. There is no need to cut benefits in the next 75 years if growth is higher.

Put simply, there is no scenario in the 2004 Trustee report where higher growth by itself will lead to 75 year solvency, let alone a stable long-run Trust Fund ratio.

Tom -- although what you suggest is, I think, possible, I'm not sure it is particularly plausible. With a slowly growing workforce, I think the more likely scenario would be for firms to invest more heavily in Capital, thereby reducing its marginal product.

Dunno. All of the models that I know about on this topic (which doesn't say much) seem fundamentally limited in a severe way, somewhere. For just one example, I don't know of a single steady-state model that can explain the 200 years of per-capita GDP growth that we've experienced.

In leiu of a model, the Trustees are basically base everything off of history except for population growth. Dean Baker et. al. argue that this exception is critical, but their argument seems to be based on reasonably restrictive models.

Regardless, it is quite possible that the killer assumption is in the earnings to GDP ratio assumption, as you seem to suggest.

I also tend to wonder ... what if you had a simple economy with a finite quantity of inter-temporal assets? As wages rise, demand for these assets will increase, even if they aren't commensurately more productive. This is basically the argument that suggests a constant P/E ratio may not be reasonable. Maybe the answer is a "bit here and a bit there", if you get my drift.

All in all, I really haven't seen a convincing case for taking these quite imperfect academic models quite literally, which is yet another thing that Dean Baker et al seem to be advocating. General compatible is something to look at, certainly, but I think the critics are going overboard.

The 'low cost' model does in fact predict no problems for SS for the next 75 years. Yes, it includes more than just higher growth. It also includes greater immigration. But a) we don't know what the actual immigration rates will be and b) even the higher growth rates of 'low cost' scenario are lower than the historical averages.

The bottom line is that the SSA admits that higher growth will improve SS's position. How much will depend on the growth rate and other conditions. And many, of not all of these conditions are difficult to predict 20 years from now, much less 75 years into the future.

I am having a devil of a time explaining this, and the result certainly does fly counter to people's intuition, since there are so many reasons that Growth is Good.

Maybe the easiest way to explain it would be on the micro level (I am thinking out loud here). Remember the old joke - two brothers are running a hat store. John says, hey, we are losing a dollar on every hat we sell. To which James repies, don't worry, we'll make it up on volume.

Most people know why that is a joke (and the rest became internet stock analysts). And yes, there are scenarios where that pricing strategy might be rational. But by and large, increasing the scale of a bad operation does not routinely make it a good operation.

Similarly with capital - to revise the joke, John would say, gee, we have ten workers running ten machines and our return on capital is terrible. To which James would reply, hire more workers and buy more machines - we'll make it up on growth.

At the micro level, "everyone knows" that if the return on capital to new investment is not adequate, you don't do it, even if the project shows positive income and would produce in profit growth.

Or, in the case of John and James, hiring more workers and buying more machines could improve the return on capital if there were significant fixed charges that did *not* have to be scaled up. But in that case, you would have to model an increase in the income share to capital (we are back to the macro forecasts) - the model would (probably) not have a default assumption that the return on capital would rise as the operation was scaled up.

So, at the micro level, "growth" does not always increase return on capital. So why do we all assume that it must at the macro level?

And did anyone even check to see if it did in the "high growth" forecasts? If the income share to capital is the same, and all those new workers in the high growth scenario need capital, when did the return on capital go up?

So long as Social Security payments are indexed to current wages, productivity growth doesn't help all that much for fixing the inherent problems of not enough workers per retiree. It will, as correctly noted, go into wage increases, which will then be passed along to retirees in the form of higher payouts.

Not to say that higher productivity isn't good, of course. Being richer and paying out more is certainly better than paying out less. But as long as the current indexing scheme is used, it's very hard to grow our way out of the problem; any growth is diverted automatically into higher Social Security payments.

Pat and Jim go into business of buyin' cheap chickens right off the farm, then haulin' 'em into town where the butcher pays better prices for 'em. Pat bargains to get 'em four for a dollar -- Jim negotiates a price with the butcher to deliver 'em at a quarter apiece.

After a while they notice they ain't makin' no money.

But they figger out what to do -- they start scrapin' up funds to buy a bigger truck!

The utility of this particular joke is that the prices can be adjusted so a profit is possible -- say the farm price is FIVE for a dollar. So they're making five cents per bird and if maybe the old truck holds a hundred birds they earn 5 dollars a trip. If they could get the bigger truck -- investing more capital -- the labor to load and unload would increase but the greater share of labor --driving to town -- would be the same. So overall the return to labor would go up and the bigger truck idea looks sound. But if the interest rate on the truck loan is higher than the 20% rate of return on chicken-truckin' then maybe what these guys really need is a bigger CLUE...

The last time I looked, the long term return on stocks was around nine percent, counting dividends and interest. I don't think there's ever been a twenty year period when it didn't beat the "inflation plus three percent" that Krugman and DeLong want to stick us with.

In either scenario, my very strong impression is that "the problem" is kicked down the road, in the sense that, for example, the date of trust fund exhaustion is pushed back.

Now, even if that is true, that *may* not be the best benchmark for declaring Soc Sec to be "saved". And it *may* be true that all we have done is push the problem past the 75 year forecast horizon, and that, if a longer view were taken, we would see that higher productivity defers, rather than "solves" the insolvency problem.

AT this point, I have not studied that carefully, and it is secondary to what I am saying here. In my casual usage, more workers "save" Social Security in the sense that they defer exhaustion of the trust fund.

(AND yes, I am well aware of the illusory nature of the trust fund as anything other than an accounting mechanism. PLEASE don't start with that.)

It's a little different than that. Actually, more productive workers getting paid more today means higher wage-indexed benefits today as well. The wage-indexing works two ways, one to compute AIME based on wages earned in one's most productive years, and another to computer benefits based on one's AIME. It's most significant for determining the cutoff points where one is effectively taxed for earning too much; benefits decrease as a proportion of original wages as they increase.

A extremely simplified version of the process:

1) Determine someone's average wage throughout their life, using some indexing formula to compare wages in different years, and to compute how much money that would be worth today. Currently we wage-index, which means that we compare, say, a 50th percentile income then to a 50th percentile income now, rather than indexing by inflation and keeping standard of living the same. Retirees now share in the general increase in wealth.

2) Tax this income in order to provide appropriate benefits, based on brackets that also rise (currently) in a wage-indexed manner. Again, retirees now share in the general increase in wages now.

That's a wages vs. compensation issue.
The share of income going to labor has been remarkably stable, and still is so. However, the percentage of total compensation taken up by benefits has increased markedly, which has caused the cash portion of compensation, wages, to be stagnant. People are familiar with the rising cost of medical insurance, of course, but there have been other rising costs, such as increased family leave, etc. (This is why laws mandating leave and certain benefits usually help some workers by costing others; the costs of benefits comes out of wages in the end.)

Actually, I'm not certain which one SS indexes based on; I'll have to check. If SS indexes based on wages, then the growth in benefits as a proportion of compensation is a back-door solution to the problem. Actually, it may well index based on wages, since Medicare covers what is often the largest part of compensation. (along with things like paid leave and vacation, which don't really apply to retirees.)

"My forecast works if we have flat real wages for a few years, while capital scoops up the income associated with higher productivity.

"IS my forecast that implausible?"
~~~~~~

You need some mechanism to keep firms from using up their increased profits by bidding up the price of labor as they compete for the employees they want, and so winding up back where they started in the original equilibrium.

You need some mechanism to keep firms from using up their increased profits by bidding up the price of labor as they compete for the employees they want, and so winding up back where they started in the original equilibrium.

Well, not if we are not currently at equilibrium - if current returns are 5%, and folks are happy with that, then so be it. But if folks really want a higher return on capital, a period of cost-cutting is in the cards.

While I was almost overpowered by the sheer intellectual power of your argument (I think it was: Luskin is stupid because Brad DeLong says so), I did actually read the DeLong post. He completely sidesteps the point.

Yes, if someone retires now and that person's future payouts are indexed to inflation, then productivity growth will help with that individual's future claims on the system. But what about people who retire in 40 years? Their payouts will be set initially based on wage levels at that time, just as payroll taxes into the system will be. So with higher growth, we have both higher payments to the system and higher payouts.

I think both you and DeLong would do better to avoid calling everyone stupid every chance you get. This is especially true in DeLong's case. He routinely accuses his opponents of stupidity, then fails to address their arguments. You will note, I never accuse Krugman of stupidity, just dishosesty and rabid partisanship.

I have to thank GT for suggesting reading the Social Security Trustees report. It was interesting.

The low cost model GT mentions does include higher prductivity growth. It also includes higher immigration, an increase in the birth rate per woman from current levels, and a decrease in the rate at which the death rate is currently declining. So, yes, if the U.S. lets in more immigrants, everyone has more babies, and technology stops increasing our life span as fast as it is increasing it now, then increased productivity gets us out of the projected mess.

Let me justsay that I mustbe pretty stupid too, for as couple of reasons.

First, as to the intuition, higher productivity means that payroll tax receipts go up today (good for Soc Sec trust fund) but wage-indexed benefits go up down the road.

IS it immediately and painfully obvious that over the long life of the Soc Sec Trust Fund, this can only help? Or is it possible that it simply pushes the problem down the road? The answer to that does not jump out at me.

But it is immediately obvious that if you stop the analysis at a 75 year point, you may underestimate the "back-end pain".

SO, until 5 minutes ago, I was open on this question. And I had read Brad DeLong's post (Dean Baker had one too), and neither one was compelling.

However! Having put together the smallest of spreadsheets, I am satisifed that higher productivity helps Soc Sec finances, even allowing for back-end effects.

Which may allow one to wonder why Don Luskin did not do something similar. Hmm.

Well, OK, that is the new official editorial position - productivity growth can save Soc Sec, not simply defer the pain. Nice to know, especially since so many others think so.

(The key to my spreadsheet is that this is a pay as you go system - the higher receipts as productivity rises are matched against current benefits that are not changing. I set up a simple one worker, one retiree system; after twenty years, the original retiree dies, the worker retires, and a new worker replaces him.

With no inflation, the initial receipts from Worker 1 are set equal to the benefits to Retiree 1. With wage increases, the receipts rise, but not the benefits due Retiree 1. This produces a Soc Sec surplus which gets bigger with higher wage increases.

When Retiree 1 dies and Worker 1 becomes Retiree 2, we get a new Worker 2, who joins the workforce at the retiring wage of the old Worker 1. And the cycle repeats - Worker 2 gets productivity raises, raising Soc Sec receipts, but Retiree 2 does not.

Or, if you halt the productivity increases, then the receipts from Worker 2 match the benefit due Retiree 2, and the trust fund balance stays put.

First, wage increases now increase the benefits due Retiree 1 because current wage level, not inflation, is used to determine the present value of Retiree 1's benefits based on the amount earned during his life. Second, wage increases now increase the "bend points," which are indexed to current wages. A retiree gets back 90% of imputed benefits to the first bend point, 35% between the first and second, and then 10% up to a maximum past the second one. Imagine them as tax brackets of 10%, 65%, and 90% off of benefits. Wage indexing indexes the brackets, so rising wages decrease the effective tax paid.

Once your initial payouts are set, the rate of increase is the rate of increase in average wage growth, NOT inflation. This is what the big deal about the proposed change from wage-indexing to inflation-indexing for benefits is all about. Currently, increased wages today are IMMEDIATELY reflected in increased benefits for EVERY retiree. If the wages rise 5%, then so do benefits, and there's no win, not even short term.

Further to John Thacker's thoughts. Look at the Trustees' report. Their scenario in which SS faces no long term problem assumes not just higher productivity, but essentially assumes away the entire demographic issue. Sure, if society does not get older over time, we are fine. But that is a not a conservative assumption.

GT, I read the DeLong post and he simply does not adequately address the wage indexing problem. He sets up an example that does NOT match the current law, and that ignores workers retiring in the future, and says the system is fine.

GT 5:40 AM: I'll answer for TM ... that is indeed how it works. As to Estimate I from the Trustees (the "low cost" scenario), I think other readers have done an excellent job of describing my perspective on it. I will only point out that the stochastic modeling done by the Trustees indicates that the "low cost" model was so improbable that it fell outside the 95% confidence range of all scenarios. This is in contrast to the "high cost" model which was within that range, unfortunately.

TM 9:25: I agree. More productivity helps, but it helps mainly because of timing: you put more tax revenue into the system before you take the benefits out. Essentially, more productivity can be viewed as a substitute for higher fertility; they have the same effect (albeit with slightly different lags).

Also notice that the Trustees always do a sensitivity analysis on the real-wage differential that tells us how productivity affects solvency. VoxBaby took those calcs home and the bottom line is that no reasonable increase in productivity, alone, can get you to solvency. And, of course, the Trust Fund ratio is an important indicator; productivity improvements can help it, but not entirely fix it. Social Security solvency is best viewed as a demographic problem, not an economic one.

One item on the subject that has gone unmentioned, however, is that productivity is also volatile, at least historically. Especially the way the Social Security Trustees calculate it, it's essentially a residual: GDP divided by the workforce. What I'm getting at here is that you could easily have a "productivity boom" that mirrors the "baby boom". In point of fact, we effectively had a "productivity recession" from 1973-1993ish that exacerbated the Social Security crisis. That explains why the Actuarial projections after the 1983 reforms deteriorated so rapidly.

If we increase the productivity assumption (which we probably should) we should also be aware, therefore, that we have increased downside risk. Privatization opponents, to date, have not discussed this and seem to pretend that higher assumed productivity is costless in much the same way that privatization supporters suggest the equity premium is costless. Ironies abound.

Pete, my spreadsheet is so simple I am embarrassed to say more - I assume one worker and one retiree, and every twenty years (totally arbitrary) the retiree dies, the worker retires, and a new worker emerges.

As a further simplification, there is no inflation; the new retiree's benefit is fixed at his last "taxes paid"; consequently, when the new worker comes on at the old workers wage, the new workers "taxes paid" covers the benefit due the new retiree.

Subsequently, the new worker gets raises, but the retiree does not - trust fund surplus grows!

It's simple and illustrative, and I suspect that some sort of a bulge in retirees could throw things off. But I would be inclined to blame the problems on the bulge itelf, rather than the indexing. My conclusion is that if we had a demographic steady state, wage indexing would be stable to helpful.

If we don't have a steady state demographically, problems may arise, and it may be possible to solve those problems by jiggling the wage indexing, but that does not mean (to me, right now anyway) that wage indexing is the problem. I am trying to take a long view, and we won't be having baby booms and busts forever.

It must come down to different definitions of what the problem is. To me, we are looking at a continually aging population, and, therefore, a continuing demographic problem in Soc Sec. Could productivity growth solve the problem if the demographic change disappeared? Sure. I just don't see the demographic problem going away.